Local magnitude, coda magnitude, and radiated energy of volcanic tectonic earthquakes from October 2010 to December 2011 at Sinabung volcano, Indonesia

In August 2010, Sinabung volcano began erupting after more than a thousand years of dormancy. Following several weeks of phreatic eruptions, the eruptions ceased and Sinabung entered what became an inter-eruptive period of dominantly seismic unrest. While standard equations for understanding the size of an earthquake (local magnitude (M_L), coda magnitude (M_C), and seismic energy release (E_R)) have long been developed, it is best practice to fine tune these relations for a given region and period of study to more accurately describe seismicity and to directly compare it with other volcanic systems. More accurate descriptions of magnitudes and energy release are vital to accurate volcanic eruption forecasting and evaluation of seismic and volcanic risk. In this study, we use high-frequency volcano-tectonic (VT) earthquakes recorded on a temporary three-component network installed between October 2010 and December 2011 in the region around Sinabung volcano to better constrain the seismic parameters of and better understand this previously unstudied volcano. We determine region-specific formulas for M_L, M_C, and E_R as follows:

where A, r, and t_coda are maximum amplitude on a Wood-Anderson seismogram, hypocentral distance (km), and the coda duration (s), respectively. Constants in the M_L equation have physically interpretable meanings. The constant for the geometrical spreading term (log₁₀r term) equals one for perfect spherical spreading of the waveform. Our value is greater than one and thus suggests that wavefronts spread at a slightly different rate than for simple spherical spreading. The constant for the attenuation term (r term) is consistent with locally mapped attenuative deposits (limestones and tuffs) and previous 3D tomographic results. Our M_C equation differs from a previous study, likely because different data in a different time period were used. Earthquake hypocenters are consistent with those located in previous tomographic studies, and we interpret the earthquakes in this study as distal VT earthquakes induced by continued magmatic intrusion at Sinabung over the period of October 2010–December 2011.